P1.15
Comparison of Potential Vorticity Diagnosis using Quasigeostrophic and Nonlinear Balance Systems
John W. Nielsen-Gammon, Texas A&M University, College Station, TX; and D. A. Gold
The diagnosis of midlatitude weather systems is performed primarily using concepts and techniques from quasigeostrophic theory, despite the availability of more sophisticated techniques, powerful workstations, and a limited range of theoretical validity. As has been noted before, quasigeostrophy generally gets the right answer even when it's not supposed to. The framework for diagnosis has been the omega equation and, to a somewhat lesser extent, the height tendency equation.
Over the past fifteen years, a new diagnostic framework has emerged based on potential vorticity. In addition to qualitative "potential vorticity thinking", quantitative techniques have been developed for diagnosis and understanding of midlatitude weather systems. These techniques involve both inversion of elements of the potential vorticity distribution -- piecewise potential vorticity inversion -- and inversion of elements of the potential vorticity tendency equation -- piecewise tendency diagnosis. In the quasigeostrophic limit, the potential vorticity tendency equation is simply the quasigeostrophic height tendency equation cast in a new light.
Although there have been many comparisons of quasigeostrophic and less approximate forms of the omega equation and its performance in real-world situations, we here perform the first quantitative comparison of diagnoses of potential vorticity tendency using quasigeostrophic and a recently-developed form of nonlinear balance diagnosis.
Quasigeostrophic (or pseudo-) potential vorticity is known to be a scaled, approximate form of Ertel potential vorticity. Looking closely at the nature of the approximations, we consider four. First, Ertel potential vorticity includes the ageostrophic vorticity, which because of gradient wind balance weakens the amplitude of cyclones and increases the amplitude of anticyclones. Second, Ertel potential vorticity includes the product of perturbation vertical vorticity and perturbation vertical stratification. Third is a tilting correction term, which quantifies the difference between vorticity on isentropic surfaces and vorticity on quasi-horizontal surfaces. Finally, there is a term proporitional to the perturbation temperature itself, scaled by the specific density. Together, these terms cause differences between the Ertel and quasigeostrophic potential vorticity that can be of great dynamical significance in circumstances where small but nozero horizontal gradients of potential vorticity are of fundamental importance. For example, a tropopause-based vortex with zero Ertel potential vorticity anomaly in the troposphere will have a positive quasigeostrophic potential vorticity anomaly in the troposphere because of the ageostrophic vorticity term.
The inversion of potential vorticity also produces differences. Because of the inversion operator, there will be differences related to horizontal variations of the background vorticity and stratification, which impacts the nonlinear balance inversion but not the quasigeostrophic inversion. More systematically, there are differences in the vertical penetration of anomalies. Perturbation heights decay upward much more rapidly in the nonlinear balance system than the quasigeostrophic system. As a result, there will be a quantitative difference between the quasigeostrophic and nonlinear balance systems in the attribution of particular height anomalies to particular potential vorticity anomalies.
With regard to diagnosis of height tendencies at upper levels, nonlinear balance is much more accurate than quasigeostrophy, but the spatial patterns of tendencies are sufficiently similar that one might hope that quasigeostrophic diagnosis would yield a qualitatively correct view of the dynamics, at least until the weather system becomes very strong. A detailed comparison of individual terms confirms this supposition.
At lower levels, ageostrophic processes and the likely strong impact of diabatic processes cause a fundamental divergence between piecewise quasigeostrophic tendency diagnosis and nonlinear balance diagnosis. We conclude that the surface height tendencies in a rapidly developing extratropical cyclone should not be diagnosed using quasigeostrophic potential vorticity because fundamental errors of interpretation are likely to result.
Poster Session 1, General Poster Session (Hall 4AB)
Monday, 12 January 2004, 2:30 PM-4:00 PM, Hall 4AB
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